1. Field of the Invention
The present invention relates to a method and a program of analyzing a process window in a lithography process.
2. Description of the Related Art
In a manufacturing process for semiconductor devices, lithography is used as a technique for forming a fine circuit pattern (hereinafter, “pattern”) on a wafer. In a lithography process, photosensitive resin (resist) is applied over the wafer and the pattern is transferred onto the wafer by using an exposing apparatus. In transferring the pattern, to secure a desired property of the semiconductor device, it is necessary to control the dimensions of the transferred pattern to be set within an allowable range determined from design conditions.
The dimensions of the pattern can be adjusted according to an exposure amount and a focus position in an exposing process. Therefore, in work called exposure condition setting in the lithography process, exposure processing is actually applied to the wafer with the exposure amount and the focus position changed and the dimensions of a formed pattern is measured to obtain optimum values of the exposure amount and the focus position. In obtaining optimum values, a range (a process window) concerning the exposure amount and the focus position for setting the dimensions of the pattern within an allowable range is created. Center values of the process window are set as the optimum values. In other words, the process window represents an allowable range including the optimum values concerning the exposure amount and the focus position.
When process window for lithography is experimentally obtained, the exposure amount and the focus position are changed on one wafer and an exposure position is simultaneously moved, exposure processing is carried out a plurality of times, and the dimensions of patterns formed in the exposure processing are measured respectively. Samples are created for a plurality of different sets of exposure amounts and focus positions. The exposure positions on the wafer are moved to prevent exposure shots from overlapping one another. To sufficiently open the process window, it is necessary to appropriately set ranges of change in the exposure amounts and the focus positions in performing the sample creation. In other words, it is necessary to appropriately set the ranges of change to include the process window. For that purpose, in the creation of sample patterns, it is desirable to, for example, allocate the exposure amounts and the focus positions such that an exposure amount and a focus potion giving optimum dimensions are present near the center of the wafer, i.e., present in the center of the ranges of the changed exposure amounts and focus positions.
However, when a shot size is large, a method of allocating the exposure amounts and the focus positions may be inappropriate and the ranges of change in the exposure amounts and the focus positions may be inappropriate. In other words, the exposure amount and the focus position giving the optimum dimensions may deviate from the center of the wafer.
In such a case, an experiment only has to be performed again to create samples again such that optimum dimensions are formed in the center of the wafer. However, an experiment often cannot be performed because of time and cost. Therefore, measured dimensions only have to be extrapolated to calculate a process window for lithography. However, in the past, reliability of the extrapolation is not clearly defined. For example, a method of improving a model for fitting measured dimensions as a curve is described in Chris A. Mack and Jeffery D. Byers, ‘Improved Model for Focus-Exposure Data Analysis’, Metrology, Inspection, and Process Control for Microlithography XVII, Daniel J. Herr, Editor, Proceedings of SPIE, Vol. 5038, pp. 396 to 405 (2003). However, even if such a model is applied to create a process window and extract exposure conditions, the exposure conditions may be outside an allowable range because reliability of an extrapolation range is unclear. Therefore, when semiconductor devices are manufactured by using such inappropriate exposure conditions, yield cannot be secured.